Page 233 - Introduction to Computational Fluid Dynamics

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Cylinder 0 521 85326 5 2D CONVECTION – COMPLEX DOMAINS
Boundary
P
B Figure 6.33. Cells near the cylinder boundary.
X 2
X 1
Symmetry Axis

averaged heat transfer coefficients at the cylinder surface after a converged
temperature solution is available? The temperature of the fluid entering the
channel is T in whereas the channel walls are maintained at T wc . Write the ex-
pressions in discretised form. The heat transfer coefficient is defined as h =
q w /(T w − T ref ). What should be the relevant reference temperature T ref for this
problem?
19. In the study of boundary layer development in the presence of favourable pres-
sure gradients, an apparatus shown in Figure 6.34 is constructed. It is then
assumed that in the presence of a sloping wall, the local free-stream velocity
varies as U ∞ (x) = U o (1 + x/L). An analyst desires to verify this assumption
by carrying out computation of the flow from entry to exit as an elliptic flow and
allowing for the presence of the plate of thickness t. The following information
◦
is given: U o = 1.8 m/s, L = 1m, H = 0.7 m, and air is at 30 C and 1 atm.
(a) Write the equations and the boundary conditions governing the flow. Hence,
identify the relevant s assuming turbulent air flow.
(b) Which turbulence model will you use? HRE or LRE?
(c) Which type of grid will you prefer? Curvilinear or unstructured?

Sloping Wall

U o H U (x)
8
H
2
Boundary Layer Development
in favourable pressure gradient
x
L

Figure 6.34. Boundary layer development in a wind tunnel.